Some Generalized Gronwall-Bellman Type Impulsive Integral Inequalities and Their Applications

This paper investigates some generalized Gronwall-Bellman type impulsive integral inequalities containing integration on infinite intervals. Some new results are obtained, which generalize some existing conclusions. Our result is also applied to study a boundary value problem of differential equations with impulsive terms

Existence of Generalized Homoclinic Solutions of Lotka-Volterra System under a Small Perturbation

This paper investigates Lotka-Volterra system under a small perturbation vxx=-μ(1-a2u-v)v+ϵf(ϵ,v,vx,u,ux), uxx=-(1-u-a1v)u+ϵg(ϵ,v,vx,u,ux). By the Fourier series expansion technique method, the fixed point theorem, the perturbation theorem, and the reversibility, we prove that near μ=0 the system has a generalized homoclinic solution exponentially approaching a periodic solution

The <inline-formula> <graphic file="1687-1812-2009-173028-i1.gif"/></inline-formula> Solutions of the Series-Like Iterative Equation with Variable Coefficients

By constructing a structure operator quite different from that ofZhang and Baker (2000) and using the Schauder fixed point theory, the existence and uniqueness of the solutions of the series-like iterative equations with variable coefficients are discussed.</p

The C1 Solutions of the Series-Like Iterative Equation with Variable Coefficients

By constructing a structure operator quite different from that of Zhang and Baker (2000) and using the Schauder fixed point theory, the existence and uniqueness of the C1 solutions of the series-like iterative equations with variable coefficients are discussed

Exploration of Optical Properties of Novel Pyrene Derivatives Modified by Click Functionalization

A simple synthetic method was designed, in which the Sonogashira coupling reaction and [2+2] cycloaddition click reaction with high yield were performed on 1-bromopyrene to obtain several novel pyrene derivatives. The structure of each sample was characterized by Nuclear Magnetic Resonance (NMR), Mass Spectrometry (MS), Fourier transform infrared (FTIR) and elemental analysis. The characterization of the products by Ultraviolet-visible (UV-vis) and Photoluminescence (PL) spectroscopy proves that the addition of click groups has an important effect on the optoelectronic properties of pyrene derivatives. The Z-scan technique was used to test the third-order nonlinear optical (NLO) properties of the samples, and it could be found that the NLO properties of the products were improved and the transition of saturable absorption and reverse saturable absorption occurred with the addition of click reagent. These factors indicate that the click-modified pyrene derivatives have potential applications in areas such as optical limiting

Hydrogen Bond-Directed Self-Assembly of a Novel Pyrene Derivative

A symmetrical pyrene derivative chemical structure was prepared by a classical synthetic method such as the Sonogashira cross-coupling reaction. The molecular structure of the product was characterised in detail by nuclear magnetic resonance (NMR), mass spectrometry (MS) and other methods. Furthermore, the optical properties of the novel products were studied by UV-vis and photoluminescence spectroscopy. The electrochemical properties of the molecules were fully characterised by comparison of electrochemical experiments and DFT simulation. Scanning electron microscope (SEM) observed that the product successfully formed a regular self-assembly structure. The product verifies the role of the molecular structure of the disc-mounted molecules on the optical and self-assembly properties, and is of reference value in the field of organic optoelectronic molecule

QTL of fiber quality and yield related traits mapped in the linkage map.

<p>Note: (+) indicates a positive additive effect; * indicates that the QTL could be identified in the two populations.</p